Generation of n-body entangling interactions between qubits

Abstract

Systems and methods for producing N-body entangling interactions to simplify n-gate operations in quantum computing applications are disclosed herein. According to at least some embodiments, an oscillator generates a two-tone field tuned to qubit resonance, first upper motion-induced sidebands, first lower motion-induced sidebands, second upper motion-induced sidebands, and second lower motion-induced sidebands.

1 . A method for generating an N-body entangling interaction between qubits in a quantum computing system, comprising:
 configuring one or more parameters for each of a plurality of pulses to be individually applied to a plurality of target ions in a chain of trapped ions as a series of displacement operations and qubit state-dependent squeezing operations on each of the target ions, each of the trapped ions in the chain defining one of the qubits of the quantum computing system;   generating, based on the one or more parameters, each of the plurality of pulses; and   applying the generated pulses to the plurality of target ions to create an entanglement interaction between the target ions.   
     
     
         2 . The method of  claim 1 , wherein configuring the one or more parameters comprises configuring a tuning frequency and amplitude of the pulses to drive one or more properties associated with each of the target ions. 
     
     
         3 . The method of  claim 2 , wherein to drive the one or more properties associated with each of the target ions comprises to drive a quantum state of the respective qubit. 
     
     
         4 . The method of  claim 2 , wherein to drive the one or more properties associated with each of the target ions comprises to drive a motion of the respective qubit. 
     
     
         5 . The method of  claim 2 , wherein to drive the one or more properties associated with each of the target ions comprises to drive motional transitions for generating the series of displacement and qubit state-dependent squeezing operations. 
     
     
         6 . The method of  claim 1 , wherein each of the displacement operations occurs simultaneously with each of the qubit state-dependent squeezing operations. 
     
     
         7 . The method of  claim 1 , wherein each of the displacement operations and the qubit state-dependent squeezing operations occur in a specified sequence. 
     
     
         8 . The method of  claim 1 , wherein each of the displacement operations occur in a sequential and interleaved manner relative to the qubit state-dependent squeezing operations. 
     
     
         9 . The method of  claim 1 , wherein the displacement operations are qubit state-dependent. 
     
     
         10 . A method for generating an N-body entangling interaction between two or more target qubits of a plurality of qubits in a quantum computing system, comprising:
 generating, by an oscillator of the computing system and for each target, a plurality of a single-tone or multi-tone fields, a first field driving the qubit between its quantum states, a second field driving the motion of the qubit, a third field driving first motional sidebands of the qubit, and a fourth field driving second motional sidebands of the qubit to apply a series of displacement forces and qubit state-dependent squeezing forces on the qubit to entangle the qubit with the other target qubits.   
     
     
         11 . The method of  claim 10 , wherein the application of the displacement forces occurs simultaneously with the application of the qubit state-dependent squeezing forces. 
     
     
         12 . The method of  claim 10 , wherein the application of displacement forces and qubit state-dependent squeezing forces occur in an interleaved manner within one another. 
     
     
         13 . The method of  claim 10 , wherein the displacement forces are determined based on H D =ℏA(x sin ϕ D +p cos ϕ D ) and wherein the squeezing forces are determined based on H S =(e −iδ   sϕ â 2 −e iδ     ϕ   â \2 ). 
     
     
         14 . A quantum computing system, comprising:
 one or more processors;   a chain of trapped ions, each of the trapped ions defining a qubit;   one or more lasers configured to emit a laser beam that is split into two or more non-copropagating laser beams which are provided to each of the trapped ions;   a controller comprising memory storing program code, which, when executed by the one or more processors, causes the quantum computing system to:
 configure one or more parameters for each of a plurality of pulses to be individually applied to a plurality of target ions in a chain of trapped ions as a series of displacement operations and qubit state-dependent squeezing operations on each of the target ions, each of the trapped ions in the chain defining one of the qubits of the quantum computing system; 
 generate, based on the one or more parameters, each of the plurality of pulses; and 
 apply the generated pulses to the plurality of target ions to create an entanglement interaction between the target ions. 
   
     
     
         15 . The quantum computing system of  claim 14 , wherein to configure the one or more parameters comprises to configure a tuning frequency and amplitude of the pulses to drive one or more properties associated with each of the target ions. 
     
     
         16 . The quantum computing system of  claim 15 , wherein to drive the one or more properties associated with each of the target ions comprises to drive a quantum state and/or a motion of the respective qubit. 
     
     
         17 . The quantum computing system of  claim 15 , wherein to drive the one or more properties associated with each of the target ions comprises to drive motional transitions for generating the series of displacement and spin-dependent qubit state-dependent squeezing operations. 
     
     
         18 . The quantum computing system of  claim 14 , wherein each of the displacement operations occurs simultaneously with each of the qubit state-dependent squeezing operations. 
     
     
         19 . The quantum computing system of  claim 14 , wherein each of the displacement operations and the qubit state-dependent squeezing operations occur in a specified sequence. 
     
     
         20 . The quantum computing system of  claim 14 , wherein each of the displacement operations occur in a sequential and interleaved manner relative to the qubit state-dependent squeezing operations.